Wayne Gretzky is a perfect fit for the Capitals, The Post's Larry Brooks says. The team's coach and GM were ousted last week after the Caps failed to make the playoffs for the first time since 2007. Photo: Getty; Startracks

PITTSBURGH — In the District of Columbia, the presidency awaits Wayne Gretzky … if Capitals owner Ted Leonsis recognizes the need to restructure the front office of his drifting franchise, that is.

Sources have told Slap Shots though there is “mutual interest” between Leonsis and Gretzky in the wake of the firing of general manager George McPhee, and head coach Adam Oates, No. 99’s interest is in the position of President of Hockey Operations, which the owner has yet to commit to creating.

It is the new model in the NHL. Brian Burke in Calgary is president overseeing the GM. Trevor Linden in Vancouver not only is conducting a search for the GM to replace Mike Gillis, he also is drawing up a list of candidates to replace John Tortorella behind the bench. Brendan Shanahan in Toronto appears to have been given a wide swath to overhaul the front office operation of the Maple Leafs, as well as the coaching staff, should he so choose.

The Caps are in need of a hockey leader with the authority to catch Alex Ovechkin’s attention and change the culture in Washington. They are in need of an individual with an advanced degree in championships. They are in need of Dr. 99.

Gretzky’s interest in returning to the NHL in a full-time role is keen, but he is not interested in becoming a general manager. The Caps have a president in Dick Patrick — who is part owner and alternate governor and who has been intimately involved in hockey decisions for a couple of decades. If Leonsis were to hire Gretzky, Patrick clearly would have to yield a fair amount of his power.

A coach reporting to a GM who reports to the president of hockey ops who reports to the president who then reports to the owner entails one too many levels and creates a power structure in which no one can truly be held accountable

Stanley Cups cannot be won without accountability. One thing to know about Gretzky — if given the authority, he will be accountable.

The Caps — or any team, for that matter — should not hire Gretzky for his name value, or to have him shake hands with the paying customers on the concourse. Leonsis should not hire him as a PR move. The value of those moves is always short-lived.

In Vancouver, Linden may be a hero at this moment, but if the Canucks flounder for the next few years, his wonderful playing career will mean nothing and he will be gone. See: Knicks and Willis Reed; also Dave DeBusschere.

No, Gretzky should be hired for his knowledge and his vision. And even if he has been away from the game for a while (too long of a while, in fact) in an official capacity, he has maintained a network of capable people throughout the industry loyal to him and from whom he would draw to restructure the Caps’ operation that clearly needs a new direction.

Gretzky is not about to launch a campaign for the job. But if did, the posters would be pretty neat. They would read, “The Great One for President.”

There is not even an ounce of pleasure, gratification or satisfaction derived in this space from chronicling Tortorella’s professional demise. Our very public confrontations were the tip of an iceberg. So much more was unseen. I will share this: At the start of the 2012-13 season when I had a medical issue, Tortorella was kind, caring and compassionate. That holds more meaning than being professionally disrespected.

Something has gone terribly wrong with Tortorella as an NHL head coach. Being fired twice within 11 months should disabuse him of the notion that someone else was to blame. This is a man now clearly at a crossroads who requires time and counsel to get back on track as well as get back to the league.

I believe there is a place for him following a sabbatical, and I believe there will be an owner who reaches out to him, and I don’t think it would be out of the question for the as-yet-unknown Brooklyn owner to be that person, though that fellow might want to check first with John Tavares.

That, in itself, is the crux of the matter. The coach who once rode his stars to a Stanley Cup now can’t coach stars. The spot for Tortorella is with a small-market team with a low payroll featuring a core of young foot soldiers and an absence of name players who not only will run three miles for Tortorella at training camp, but will be willing to run through the walls for him on the ice.

Tortorella always has had a deep appreciation for the craft of coaching. But he stopped coaching the last couple of years. He became a zealot, and generally unpleasant to play for, alienating players from two organizations almost 3,000 miles apart with unyielding demands and an unrealistic game plan.

The game has evolved, even over the last three or four seasons. Now it is time for Tortorella to evolve. That is his only way back to the NHL and to his career.

A year ago, the Rangers were 4-for-44 in the playoffs on the power play. Now, they are 3-for-33. Come back, Mike Sullivan. All is forgiven. Well, not really.

Have just got to say, watching the handshake line between the Rangers and Flyers, Scott Hartnell went through it faster than he skated in the entire seven-game series.

I am awaiting the press release in which the NHL announces Jumbo Joe [Thornton] is the league’s official oxymoron.